Geodesic
Representations of bicircular lift matroids
The electronic journal of combinatorics, Tome 23 (2016) no. 3
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Bicircular lift matroids are a class of matroids defined on the edge set of a graph. For a given graph $G$, the circuits of its bicircular lift matroid are the edge sets of those subgraphs of $G$ that contain at least two cycles, and are minimal with respect to this property. The main result of this paper is a characterization of when two graphs give rise to the same bicircular lift matroid, which answers a question proposed by Irene Pivotto. In particular, aside from some appropriately defined "small" graphs, two graphs have the same bicircular lift matroid if and only if they are $2$-isomorphic in the sense of Whitney.
DOI : 10.37236/5677
Classification : 05B35, 05C38, 05C60, 52B40
Mots-clés : bicircular lift matroids, representation 
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     author = {Rong Chen and Zifei Gao},
     title = {Representations of bicircular lift matroids},
     journal = {The electronic journal of combinatorics},
     year = {2016},
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     number = {3},
     doi = {10.37236/5677},
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Rong Chen; Zifei Gao. Representations of bicircular lift matroids. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/5677

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